ELEMENTS OF GEOMETRY, IN GENERAL TERMS, WITH NOTES, &c. &c. ALSO, A VARIETY OF PROBLEMS AND THEOREMS, CAREFULLY ARRANGED AND SELECTED; WITH ANALYSIS. BY THE REV. J. LUBY, A. M. T. C. D. BIBLIO PRINTED FOR J. J. EKENS, 28, ANGLESEA-STREET. PREFACE. THE general objects of the present treatise being to facilitate the study of the Elements of Geometry, as well as to promote the exercise of it amongst the students as much as possible; it seems advisable to show how far the reader may presume on these objects being attained. The former is attempted by giving the propositions of the Elements general demonstrations, which must, more than any other, contribute to give the reader clear and comprehensive views on the subject of Geometry, and to cultivate his reasoning powers with respect to all parts of human knowledge. On the subject of vivá voce demonstrations, much has been said against their general use, particularly in the higher orders of Mathematics and Physics, and indeed too much could not be said, if any good were likely to result from it. Academical reform is too hopeless a case, and one of too extensive a nature, to be worth discussing at any length. In plane Geometry, however, where analytic artifice has no place, and where the reader is seldom, if ever, obliged to lose sight of the basis on which his reasoning rests, vivá voce demonstrations are of powerful effect. They accustom him to clearness and solidity of reasoning, and enable him to take a view of the whole of a subject at |